In triangle ABC, ∡A is a right angle, and m∡B = 45°
What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
A. 14square root of 2 ft
B. 28 ft
C. 14square root of 3 ft
D. 14 ft
Since ∠A is a right angle, we know that BC is the hypotenuse of a right triangle. We also know that ∠B = 45°, which means that the other two angles of the triangle are also 45° each. This makes the triangle an isosceles right triangle, where the two legs are congruent. Let's call the length of AB and AC "x".
Using the Pythagorean theorem, we can find the length of BC:
BC² = AB² + AC²
BC² = x² + x² (since AB and AC are congruent)
BC² = 2x²
BC = sqrt(2x²)
BC = x * sqrt(2)
Since we don't know the value of x, we can't simplify this any further. Therefore, the answer is:
A. 14sqrt(2) ft